covid19-lmm-forecast-draft
1 Downloading and getting data in shape
1.1 Initial work
- First need to read in all.csv off Ken’s GitHub page; to do this, load RCurl package to use getURL function w/in read.csv, as the csv file is embedded within an html file (typical for GitHub).
alldata <-
read.csv(text=getURL("https://raw.githubusercontent.com/kentranz/socialMobilityCOVID/master/data/all.csv"),
header=T)
## the above file has already been updated for standardized
## Apple mobility data, and various indicator variables for
## dates of interest, as well as lagged cases variables, etc.
## --> it has longitudinal data for 24 cities,
## 20 in US, and Toronto, Montreal, London, and Stockholm
str(alldata)## 'data.frame': 6216 obs. of 43 variables:
## $ city : Factor w/ 24 levels "Atlanta","Baltimore",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ date : Factor w/ 259 levels "2020-03-01","2020-03-02",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ newCases : int 0 2 0 0 0 0 4 4 5 4 ...
## $ casesTminus1 : int 0 0 2 0 0 0 0 4 4 5 ...
## $ casesTminus2 : int 0 0 0 2 0 0 0 0 4 4 ...
## $ drivingMinus7 : num 6.73 3.59 7.82 13.01 15.97 ...
## $ transitMinus7 : num 4.81 -2.85 3.34 4.61 12.06 ...
## $ walkingMinus7 : num 4.54 -11.14 4.76 8.71 27.63 ...
## $ drivingMinus8 : num 12.09 6.73 3.59 7.82 13.01 ...
## $ transitMinus8 : num 7.51 4.81 -2.85 3.34 4.61 ...
## $ walkingMinus8 : num 23.44 4.54 -11.14 4.76 8.71 ...
## $ drivingMinus9 : num 7.82 12.09 6.73 3.59 7.82 ...
## $ transitMinus9 : num 2.84 7.51 4.81 -2.85 3.34 ...
## $ walkingMinus9 : num 5.55 23.44 4.54 -11.14 4.76 ...
## $ drivingMinus10 : num 3.31 7.82 12.09 6.73 3.59 ...
## $ transitMinus10 : num -1.88 2.84 7.51 4.81 -2.85 ...
## $ walkingMinus10 : num 1.55 5.55 23.44 4.54 -11.14 ...
## $ drivingMinus11 : num 7.4 3.31 7.82 12.09 6.73 ...
## $ transitMinus11 : num 2.76 -1.88 2.84 7.51 4.81 ...
## $ walkingMinus11 : num 2.39 1.55 5.55 23.44 4.54 ...
## $ drivingMinus12 : num 4.48 7.4 3.31 7.82 12.09 ...
## $ transitMinus12 : num 1.55 2.76 -1.88 2.84 7.51 ...
## $ walkingMinus12 : num -8.78 2.39 1.55 5.55 23.44 ...
## $ drivingMinus13 : num 7.27 4.48 7.4 3.31 7.82 ...
## $ transitMinus13 : num 5.24 1.55 2.76 -1.88 2.84 7.51 4.81 -2.85 3.34 4.61 ...
## $ walkingMinus13 : num 6.26 -8.78 2.39 1.55 5.55 ...
## $ drivingMinus14 : num 8.11 7.27 4.48 7.4 3.31 ...
## $ transitMinus14 : num 4.49 5.24 1.55 2.76 -1.88 2.84 7.51 4.81 -2.85 3.34 ...
## $ walkingMinus14 : num 19.55 6.26 -8.78 2.39 1.55 ...
## $ driving : num 16.99 8.03 3.64 8.07 8.83 ...
## $ walking : num 26.35 -3.94 -0.85 -5.03 6.17 ...
## $ transit : num 12.27 3.27 -2.91 -4.81 1.56 ...
## $ anomalousWeekend : int 0 0 0 0 0 0 0 0 0 0 ...
## $ longWeekend : int 0 0 0 0 0 0 0 0 0 0 ...
## $ weekend : int 1 0 0 0 0 0 1 1 0 0 ...
## $ sumDrivingMinus7_14 : num 8.17 7.53 7.61 8.82 10.05 ...
## $ sumTransitMinus7_14 : num 3.9 2.85 2.58 3.02 4.35 ...
## $ sumWalkingMinus7_14 : num 7.79 3.4 3.19 5.69 9.29 ...
## $ Population : int 5950000 5950000 5950000 5950000 5950000 5950000 5950000 5950000 5950000 5950000 ...
## $ LandAreakm : int 21694 21694 21694 21694 21694 21694 21694 21694 21694 21694 ...
## $ Poverty.rate : num 13.9 13.9 13.9 13.9 13.9 13.9 13.9 13.9 13.9 13.9 ...
## $ Median.age : num 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 36.6 ...
## $ Median.household.income: num 69464 69464 69464 69464 69464 ...Code to read in data and output from
strcall hidden from this output. Most R code below for data manipulation will also be hidden from output, and only selective dataset elements will be displayed. Alternatively, R code for data analyses and resulting output will more generally be displayed.Will output variable names though:
## [1] "city" "date"
## [3] "newCases" "casesTminus1"
## [5] "casesTminus2" "drivingMinus7"
## [7] "transitMinus7" "walkingMinus7"
## [9] "drivingMinus8" "transitMinus8"
## [11] "walkingMinus8" "drivingMinus9"
## [13] "transitMinus9" "walkingMinus9"
## [15] "drivingMinus10" "transitMinus10"
## [17] "walkingMinus10" "drivingMinus11"
## [19] "transitMinus11" "walkingMinus11"
## [21] "drivingMinus12" "transitMinus12"
## [23] "walkingMinus12" "drivingMinus13"
## [25] "transitMinus13" "walkingMinus13"
## [27] "drivingMinus14" "transitMinus14"
## [29] "walkingMinus14" "driving"
## [31] "walking" "transit"
## [33] "anomalousWeekend" "longWeekend"
## [35] "weekend" "sumDrivingMinus7_14"
## [37] "sumTransitMinus7_14" "sumWalkingMinus7_14"
## [39] "Population" "LandAreakm"
## [41] "Poverty.rate" "Median.age"
## [43] "Median.household.income"Here, newCases will be converted into a rate, and this, and the first two days of lagged case rate values, will serve as the primary response and two predictors, respectively.
The time variable will be a converted version of date. This, and the previous bullet point will be worked on in the next subsection.
1.2 Additional data manipulation
- Creating a US city indicator variable, i.e., 1 if US city, 0 for non-US city.
1.2.1 Play with dates
First, note that not all 24 cities had counts available to us starting at earlier date in our dataset of March 1, 2019, while all cities had observations starting March 13th. As of the November 14th end dataset (the one being worked on here), these earlier dates in March, for cities where they were not originally collected, were entered in original dataset as 0’s. This seems a reasonable choice given the very low or non-existent case counts in many cities at that time. In addition, we will not be use data earlier than March 13th in our analyses, so those 0’s are irrelevant for our work here.
Dates are in character form, and need to change to numeric for modeling.
Need to align all new day variable to min of observed dates, so day 0 will 2020-03-01, but will have a second new day variable that will be about 2 days after 2020-03-13 (make this the midpoint of March, i.e., March 16th), to allow for two days of lagged cases as predictors; the lagged 7-day mobility data is actually available since near Feb 1, if we ever need it.
Aside from March 16th start date, we will make one for April 1st, and one that is based on a French study (Prague et al., 2020), which is dynamic based on specifically starting on the first day of cases for which it is followed by at least 3 consecutive days of cases as well; this took longer to program.
Will use chron package in R to help with dates and specifying initial origin at March 1st (day 0). As suggested on chron help page, use
optionsargument to set default first day — could do this twice to help create two sets of two columns, one where 03-01-20 is default and one for 03-16-20; a 2nd option is to subset data when modeling such that all dates are at least 03-16-20 when we want to have the later start/default date, which will only affect the intercept interpretation; will take the 2nd approach where day 15 (16th day), i.e., 03-16-20, will be first day w/ all complete data that accounts for two lagged cases days.Here is where French start day will be defined, which will be the 1st day that at least 4 consecutive days of cases start. Code will identify sequences in a vector. Output prints first day of French method in each city.
## city.FM startdate.FM
## 1 Atlanta 03/07/20
## 2 Baltimore 03/13/20
## 3 Boston 03/05/20
## 4 Chicago 03/08/20
## 5 Cleveland 03/13/20
## 6 Dallas 03/09/20
## 7 Denver 03/09/20
## 8 Houston 03/12/20
## 9 Indianapolis 03/08/20
## 10 London 03/01/20
## 11 Los Angeles 03/03/20
## 12 Memphis 03/18/20
## 13 Miami 03/10/20
## 14 Montreal 03/08/20
## 15 New York 03/04/20
## 16 Oklahoma 03/15/20
## 17 Phoenix 03/16/20
## 18 Pittsburgh 03/13/20
## 19 Portland 03/12/20
## 20 Sacramento 03/12/20
## 21 Seattle 03/01/20
## 22 Stockholm 03/01/20
## 23 Tampa 03/15/20
## 24 Toronto 03/01/20- Dec 17 2020: The above all provided, it should be mentioned that the use of the French method and start dates other than 03-16-20 will be put off for potential future use.
1.2.2 Creating case rates
- Making another column in dataset, which is a rate, i.e., number of cases per 100000 people in population. This will be the longitudinal response variable in our graphing and modeling. To do this, taking newCases, divide by Population (in city), and multiplying by 100000; will do this for caseTminus1 and caseTminus2 variables as well:
2 Start longitudinal work
2.1 Initial graphing
Start with using nlme library, created so-called groupedData objects, which benefit both graphing and modeling using the
lmefunction (and other modeling functions) within nlme.Create plots from groupedData objects; nlme generic plotting on these objects uses Trellis graphs here.
2.2 Data Partition
- We used start date as 2020-03-16, because that was the first date that allowed for at least 2 lagged observerations in all cities.
- Train set used data until 2020-10-31
- Test sets:
- test7: first 7 days in November
- test14: first 14 days in November
train <- alldata.groupedR %>%
filter(day031620 >= 0 & as.Date(date) <= as.Date("2020-10-31"))
test7 <- alldata.groupedR %>%
filter(day031620 >= 0 & as.Date(date) > as.Date("2020-10-31") & as.Date(date) <= as.Date("2020-11-07"))
test14 <- alldata.groupedR %>%
filter(day031620 >= 0 & as.Date(date) > as.Date("2020-10-31"))
nrow(train)## [1] 5520nrow(test7)## [1] 168nrow(test14)## [1] 3362.3 Automate extracting 95% CI for prediction band, metrics, and plotting
Extract 95% CI for prediction band. References from the web:
- https://stackoverflow.com/questions/14358811/extract-prediction-band-from-lme-fit and
- http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#predictions-andor-confidence-or-prediction-intervals-on-predictions
SE: This approach takes into account the uncertainty of the random effect in the prediction.
SE2: This takes into account both random effect uncertainty and within-group error
metricsFunc <- function(model)
{
# store all X and y in a new dataframe, filtering out unwanted dates
results7 <- test7 %>%
select(city, day031620, case.rate, casesTminus1.rate, casesTminus2.rate, weekend, walkingMinus7)
results7$pred <- predict(model, newdata = results7)
# create design mateix
# [-2] drops response from formula
Designmat <- model.matrix(formula(model)[-2], results7)
# compute XVX′ to get the variance-covariance matrix of the predictions
# extract the diagonal of this matrix to get variances of predictions
predvar <- diag(Designmat %*% vcov(model) %*% t(Designmat))
results7$SE <- sqrt(predvar)
results7$SE2 <- sqrt(predvar + model$sigma^2) # sigma is the estimated within-group error standard deviation
results14 <- test14 %>%
select(city, day031620, case.rate, casesTminus1.rate, casesTminus2.rate, weekend, walkingMinus7)
results14$pred <- predict(model, newdata = results14)
Designmat <- model.matrix(formula(model)[-2], results14)
predvar <- diag(Designmat %*% vcov(model) %*% t(Designmat))
results14$SE <- sqrt(predvar)
results14$SE2 <- sqrt(predvar + model$sigma^2)
# CALCULATE MAE, MAPE, CP
perform7 <- results7 %>%
group_by(city) %>%
summarize(MAE = round(mean(abs(case.rate - pred)) , 2)
, MAPE = round(mean(abs(case.rate - pred)/case.rate) , 2)
, CP = round(sum(case.rate >= (pred - 1.96*SE2) & case.rate <= (pred + 1.96*SE2) ) / n() , 2)
) #%>%
#as.data.frame() %>%
#print()
perform14 <- results14 %>%
group_by(city) %>%
summarize(MAE = round(mean(abs(case.rate - pred)) , 2)
, MAPE = round(mean(abs(case.rate - pred)/case.rate) , 2)
, CP = round(sum(case.rate >= (pred - 1.96*SE2) & case.rate <= (pred + 1.96*SE2) ) / n() , 2)
) #%>%
#as.data.frame() %>%
#print()
metrics <- perform7 %>%
left_join(perform14
, by = "city"
, suffix = c("_7d", "_14d")
) #%>%
#as.data.frame() %>%
#print()
return(list(performMetrics = metrics
, results7 = results7
, results14 = results14))
}
plotFunc <- function(model
, forecastLength # only 7 or 14 as numeric arg
)
{
if(forecastLength == 7)
{ results = output$results7
perform <- output$performMetrics %>%
select(city, contains("7d"))
}
if(forecastLength == 14)
{ results = output$results14
perform <- output$performMetrics %>%
select(city, contains("14d"))
}
perform <- setNames(perform, gsub("_.*", "", names(perform)))
perform <- perform %>%
mutate(MAPE = paste0("MAPE = ", MAPE)
, MAE = paste0("MAE = ", MAE)
, CP = paste0("CP = ", CP)
)
Designmat <- model.matrix(formula(model)[-2], train)
predvar <- diag(Designmat %*% vcov(model) %*% t(Designmat))
plotDF <- train %>%
select(city, day031620, case.rate) %>%
mutate(city = as.character(city)
, SE2 = sqrt(predvar + model$sigma^2)
, upperCI.fitted = case.rate + 1.96*SE2
, lowerCI.fitted = case.rate - 1.96*SE2
, fitted = predict(model, data = train)
) %>%
reshape::melt(id = c('city', 'day031620')) %>%
# bring into forecasted case rates
rbind(results %>%
select(city, day031620, case.rate, pred, SE2) %>%
#rename(case.rate = pred) %>%
mutate(upperCI.pred = pred + 1.96*SE2
, lowerCI.pred = pred - 1.96*SE2
) %>%
reshape2::melt(id = c('city', 'day031620'))
)
p <- ggplot(plotDF
, aes(day031620, value, group = variable, colour = variable)) +
geom_line(data = filter(plotDF, variable == 'case.rate'), linetype = "solid", color = 'black', alpha = 0.6) +
geom_line(data = filter(plotDF, variable == 'fitted'), linetype = "solid", color = 'red') +
geom_line(data = filter(plotDF, variable == 'pred'), linetype = "dashed", color = 'blue') +
# uncertainty band for fitted model
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.fitted')
, aes(ymin = filter(plotDF, variable == 'lowerCI.fitted')$value
, ymax = filter(plotDF, variable == 'upperCI.fitted')$value
)
, alpha = 0.3
, color = NA
, fill = "red") +
# prediction band for forecast
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.pred')
, aes(ymin = filter(plotDF, variable == 'lowerCI.pred')$value
, ymax = filter(plotDF, variable == 'upperCI.pred')$value
)
, alpha = 0.3
, color = NA
, fill = "blue") +
facet_wrap(. ~ city, ncol = 2) +
ggtitle(paste0('Forecast ', forecastLength, ' Days')) +
ylab('Case Rate per 100,000 People') +
xlab('Days since March 16, 2020') +
#ylim(-15,100) +
# add performance metrics
geom_label(data = perform
, aes(label = MAPE),
x = 0, y = 155, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = perform
, aes(label = MAE),
x = 0, y = 100, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = perform
, aes(label = CP),
x = 0, y = 70, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
theme_classic() +
theme(legend.position = 'none')
p
}2.4 Initial modeling, using lme function
- Aside from dealing with heteroskedasticity, the following was the best model from earlier runs, through June 30th end data at the time, starting with March 16th data. This is a linear mixed effects model, with case rate as the response, the fixed effects being the first two lagged case rate variables and the weekend indicator variable, and the random effects being the time-varying lagged case rate variables; there is no random intercept, shown not to be needed due to the relatively low levels across all cities near March 16th.
case.rate.lme20201031 <-
lme(fixed = case.rate ~ casesTminus1.rate + casesTminus2.rate + weekend,
random = ~ casesTminus1.rate + casesTminus2.rate - 1 | city,
data = train
)
summary(case.rate.lme20201031)## Linear mixed-effects model fit by REML
## Data: train
## AIC BIC logLik
## 36173.54 36226.46 -18078.77
##
## Random effects:
## Formula: ~casesTminus1.rate + casesTminus2.rate - 1 | city
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## casesTminus1.rate 0.07907325 cssT1.
## casesTminus2.rate 0.04288684 -0.435
## Residual 6.36425308
##
## Fixed effects: case.rate ~ casesTminus1.rate + casesTminus2.rate + weekend
## Value Std.Error DF t-value p-value
## (Intercept) 2.0832962 0.13890453 5493 14.99804 0
## casesTminus1.rate 0.4925352 0.02381526 5493 20.68150 0
## casesTminus2.rate 0.3444521 0.01836728 5493 18.75357 0
## weekend -1.6611538 0.19088742 5493 -8.70227 0
## Correlation:
## (Intr) cssT1. cssT2.
## casesTminus1.rate -0.216
## casesTminus2.rate -0.163 -0.613
## weekend -0.340 -0.010 -0.028
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -10.4155607 -0.3069076 -0.1145516 0.1803768 30.2216669
##
## Number of Observations: 5520
## Number of Groups: 24output <- metricsFunc(model = case.rate.lme20201031)
allMetrics <- output$performMetrics %>%
rename_at(vars(-city), function(x) {paste0(x, "_lme")})
plotFunc(model = case.rate.lme20201031
, forecastLength = 7)## Warning: attributes are not identical across measure variables; they will be
## dropped
plotFunc(model = case.rate.lme20201031
, forecastLength = 14)## Warning: attributes are not identical across measure variables; they will be
## dropped
2.5 Weighted Residual LME
Use weights to account for within-group heteroskedasticity
case.rate.lme20201031.reweighed <-
lme(fixed = case.rate ~ casesTminus1.rate + casesTminus2.rate + weekend
, random = ~ casesTminus1.rate + casesTminus2.rate - 1 | city
, data = train
, weights = varPower(form = ~ fitted(.))
, control = lmeControl(maxIter = 1e4)
)
summary(case.rate.lme20201031.reweighed)## Linear mixed-effects model fit by REML
## Data: train
## AIC BIC logLik
## 31729.12 31788.66 -15855.56
##
## Random effects:
## Formula: ~casesTminus1.rate + casesTminus2.rate - 1 | city
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## casesTminus1.rate 0.04656959 cssT1.
## casesTminus2.rate 0.05341711 -1
## Residual 1.23431392
##
## Variance function:
## Structure: Power of variance covariate
## Formula: ~fitted(.)
## Parameter estimates:
## power
## 0.6615351
## Fixed effects: case.rate ~ casesTminus1.rate + casesTminus2.rate + weekend
## Value Std.Error DF t-value p-value
## (Intercept) 0.6067788 0.05237130 5493 11.586095 0
## casesTminus1.rate 0.5251835 0.02241559 5493 23.429382 0
## casesTminus2.rate 0.4529133 0.02316650 5493 19.550361 0
## weekend -0.6734468 0.06969857 5493 -9.662276 0
## Correlation:
## (Intr) cssT1. cssT2.
## casesTminus1.rate -0.118
## casesTminus2.rate -0.085 -0.909
## weekend -0.638 0.065 -0.013
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.53641943 -0.39252666 -0.09136161 0.25386552 30.15583085
##
## Number of Observations: 5520
## Number of Groups: 24output <- metricsFunc(model = case.rate.lme20201031.reweighed)
allMetrics <- allMetrics %>% left_join(
output$performMetrics %>%
rename_at(vars(-city), function(x) {paste0(x, "_lmeWeighted")})
, by = "city"
)
plotFunc(model = case.rate.lme20201031.reweighed
, forecastLength = 7)## Warning: attributes are not identical across measure variables; they will be
## dropped
plotFunc(model = case.rate.lme20201031.reweighed
, forecastLength = 14)## Warning: attributes are not identical across measure variables; they will be
## dropped
2.6 LME Weighted Residual + Walking-7
case.rate.lme20201031.reweighed.walking7 <-
lme(fixed = case.rate ~ casesTminus1.rate + casesTminus2.rate + weekend + walkingMinus7
, random = ~ casesTminus1.rate + casesTminus2.rate - 1 | city
, data = train
, weights = varPower(form = ~ fitted(.))
, control = lmeControl(maxIter = 1e4)
)
summary(case.rate.lme20201031.reweighed.walking7)## Linear mixed-effects model fit by REML
## Data: train
## AIC BIC logLik
## 31699.57 31765.72 -15839.78
##
## Random effects:
## Formula: ~casesTminus1.rate + casesTminus2.rate - 1 | city
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## casesTminus1.rate 5.228944e-05 cssT1.
## casesTminus2.rate 3.819776e-06 0
## Residual 1.209377e+00
##
## Variance function:
## Structure: Power of variance covariate
## Formula: ~fitted(.)
## Parameter estimates:
## power
## 0.6704094
## Fixed effects: case.rate ~ casesTminus1.rate + casesTminus2.rate + weekend + walkingMinus7
## Value Std.Error DF t-value p-value
## (Intercept) 0.6707064 0.05589632 5492 11.999115 0e+00
## casesTminus1.rate 0.5166564 0.01955352 5492 26.422681 0e+00
## casesTminus2.rate 0.4551779 0.01951942 5492 23.319233 0e+00
## weekend -0.6332936 0.07090597 5492 -8.931457 0e+00
## walkingMinus7 0.0038909 0.00112549 5492 3.457094 6e-04
## Correlation:
## (Intr) cssT1. cssT2. weeknd
## casesTminus1.rate -0.156
## casesTminus2.rate -0.108 -0.870
## weekend -0.506 0.056 -0.023
## walkingMinus7 0.367 -0.058 -0.057 0.186
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.53352791 -0.39377854 -0.08448579 0.25238647 30.29984024
##
## Number of Observations: 5520
## Number of Groups: 24output <- metricsFunc(model = case.rate.lme20201031.reweighed.walking7)
allMetrics <- allMetrics %>% left_join(
output$performMetrics %>%
rename_at(vars(-city), function(x) {paste0(x, "_lmeWeightedWalking7")})
, by = "city"
)
plotFunc(model = case.rate.lme20201031.reweighed.walking7
, forecastLength = 7)## Warning: attributes are not identical across measure variables; they will be
## dropped
plotFunc(model = case.rate.lme20201031.reweighed.walking7
, forecastLength = 14)## Warning: attributes are not identical across measure variables; they will be
## dropped
2.7 Naive Multiple Regression
case.rate.lm <-
lm( case.rate ~ casesTminus1.rate + casesTminus2.rate + weekend
, data = train
)
summary(case.rate.lm)##
## Call:
## lm(formula = case.rate ~ casesTminus1.rate + casesTminus2.rate +
## weekend, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -92.542 -1.812 -0.682 1.141 190.769
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.83578 0.12889 14.243 <2e-16 ***
## casesTminus1.rate 0.47969 0.01239 38.730 <2e-16 ***
## casesTminus2.rate 0.39510 0.01242 31.810 <2e-16 ***
## weekend -1.67100 0.19383 -8.621 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.473 on 5516 degrees of freedom
## Multiple R-squared: 0.6782, Adjusted R-squared: 0.678
## F-statistic: 3875 on 3 and 5516 DF, p-value: < 2.2e-16model <- case.rate.lm
results7 <- test7 %>% select(city, day031620, case.rate, casesTminus1.rate, casesTminus2.rate, weekend)
pred <- predict(model, newdata = results7, interval = "prediction", level = 0.95) %>% as.data.frame()
results7$pred <- pred$fit
results7$upperCI <- pred$upr
results7$lowerCI <- pred$lwr
results14 <- test14 %>% select(city, day031620, case.rate, casesTminus1.rate, casesTminus2.rate, weekend)
pred <- predict(model, newdata = results14, interval = "prediction", level = 0.95) %>% as.data.frame()
results14$pred <- pred$fit
results14$upperCI <- pred$upr
results14$lowerCI <- pred$lwr
metrics <- results7 %>%
group_by(city) %>%
summarize(MAE = round(mean(abs(case.rate - pred)) , 2)
, MAPE = round(mean(abs(case.rate - pred)/case.rate) , 2)
, CP = round(sum(case.rate >= lowerCI & case.rate <= upperCI ) / n() , 2)
) %>%
left_join( results14 %>%
group_by(city) %>%
summarize(MAE = round(mean(abs(case.rate - pred)) , 2)
, MAPE = round(mean(abs(case.rate - pred)/case.rate) , 2)
, CP = round(sum(case.rate >= lowerCI & case.rate <= upperCI ) / n() , 2)
)
, by = "city"
, suffix = c("_7d", "_14d")
)
#metrics %>% arrange(as.character(city)) %>% as.data.frame() %>% print()
allMetrics <- allMetrics %>% left_join(
metrics %>%
rename_at(vars(-city), function(x) {paste0(x, "_lm")})
, by = "city"
)pred <- predict(model, newdata = train, interval = "prediction", level = 0.95)
plotDF <- train %>%
select(city, day031620, case.rate) %>%
mutate(city = as.character(city)) %>%
cbind(pred) %>%
rename(fitted = fit
, lowerCI.fitted = lwr
, upperCI.fitted = upr
) %>%
reshape::melt(id = c('city', 'day031620')) %>%
# bring into forecasted case rates
rbind(results7 %>%
select(city, day031620, case.rate, pred, upperCI, lowerCI) %>%
rename(upperCI.pred = upperCI
, lowerCI.pred = lowerCI
) %>%
reshape2::melt(id = c('city', 'day031620'))
)
p <- ggplot(plotDF
, aes(day031620, value, group = variable, colour = variable)) +
geom_line(data = filter(plotDF, variable == 'case.rate'), linetype = "solid", color = 'black', alpha = 0.6) +
geom_line(data = filter(plotDF, variable == 'fitted'), linetype = "solid", color = 'red') +
geom_line(data = filter(plotDF, variable == 'pred'), linetype = "dashed", color = 'blue') +
# uncertainty band for fitted model
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.fitted')
, aes(ymin = filter(plotDF, variable == 'lowerCI.fitted')$value
, ymax = filter(plotDF, variable == 'upperCI.fitted')$value
)
, alpha = 0.3, color = NA
, fill = "red") +
# prediction band for forecast
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.pred')
, aes(ymin = filter(plotDF, variable == 'lowerCI.pred')$value
, ymax = filter(plotDF, variable == 'upperCI.pred')$value
)
, alpha = 0.3, color = NA
, fill = "blue") +
facet_wrap(. ~ city, ncol = 2) +
ggtitle('Forecast 7 Days') +
ylab('Case Rate per 100,000 People') +
xlab('Days since March 16, 2020') +
#ylim(-15,100) +
# add performance metrics
geom_label(data = metrics %>% mutate(MAPE_7d = paste0("MAPE = ", MAPE_7d))
, aes(label = MAPE_7d),
x = 0, y = 155, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = metrics %>% mutate(MAE_7d = paste0("MAE = ", MAE_7d))
, aes(label = MAE_7d),
x = 0, y = 125, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = metrics %>% mutate(CP_7d = paste0("CP = ", CP_7d))
, aes(label = CP_7d),
x = 0, y = 70, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
theme_classic() +
theme(legend.position = 'none')
p
plotDF <- train %>%
select(city, day031620, case.rate) %>%
mutate(city = as.character(city)) %>%
cbind(pred) %>%
rename(fitted = fit
, lowerCI.fitted = lwr
, upperCI.fitted = upr
) %>%
reshape::melt(id = c('city', 'day031620')) %>%
# bring into forecasted case rates
rbind(results14 %>%
select(city, day031620, case.rate, pred, upperCI, lowerCI) %>%
rename(upperCI.pred = upperCI
, lowerCI.pred = lowerCI
) %>%
reshape2::melt(id = c('city', 'day031620'))
)
p <- ggplot(plotDF
, aes(day031620, value, group = variable, colour = variable)) +
geom_line(data = filter(plotDF, variable == 'case.rate'), linetype = "solid", color = 'black', alpha = 0.6) +
geom_line(data = filter(plotDF, variable == 'fitted'), linetype = "solid", color = 'red') +
geom_line(data = filter(plotDF, variable == 'pred'), linetype = "dashed", color = 'blue') +
# uncertainty band for fitted model
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.fitted')
, aes(ymin = filter(plotDF, variable == 'lowerCI.fitted')$value
, ymax = filter(plotDF, variable == 'upperCI.fitted')$value
)
, alpha = 0.3, color = NA
, fill = "red") +
# prediction band for forecast
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.pred')
, aes(ymin = filter(plotDF, variable == 'lowerCI.pred')$value
, ymax = filter(plotDF, variable == 'upperCI.pred')$value
)
, alpha = 0.3, color = NA
, fill = "blue") +
facet_wrap(. ~ city, ncol = 2) +
ggtitle('Forecast 14 Days') +
ylab('Case Rate per 100,000 People') +
xlab('Days since March 16, 2020') +
#ylim(-15,100) +
# add performance metrics
geom_label(data = metrics %>% mutate(MAPE_14d = paste0("MAPE = ", MAPE_14d))
, aes(label = MAPE_14d),
x = 0, y = 155, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = metrics %>% mutate(MAE_14d = paste0("MAE = ", MAE_14d))
, aes(label = MAE_14d),
x = 0, y = 125, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = metrics %>% mutate(CP_14d = paste0("CP = ", CP_14d))
, aes(label = CP_14d),
x = 0, y = 70, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
theme_classic() +
theme(legend.position = 'none')
p
2.8 Naive Multiple Regression with Walking-7
case.rate.lm.walking7 <-
lm( case.rate ~ casesTminus1.rate + casesTminus2.rate + weekend + walkingMinus7
, data = train
)
summary(case.rate.lm.walking7)##
## Call:
## lm(formula = case.rate ~ casesTminus1.rate + casesTminus2.rate +
## weekend + walkingMinus7, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -92.169 -1.811 -0.622 1.093 190.565
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.890943 0.129546 14.597 < 2e-16 ***
## casesTminus1.rate 0.476399 0.012400 38.418 < 2e-16 ***
## casesTminus2.rate 0.391947 0.012433 31.524 < 2e-16 ***
## weekend -1.619760 0.194059 -8.347 < 2e-16 ***
## walkingMinus7 0.008028 0.002107 3.810 0.000141 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.465 on 5515 degrees of freedom
## Multiple R-squared: 0.679, Adjusted R-squared: 0.6788
## F-statistic: 2917 on 4 and 5515 DF, p-value: < 2.2e-16model <- case.rate.lm.walking7
results7 <- test7 %>% select(city, day031620, case.rate, casesTminus1.rate, casesTminus2.rate, weekend, walkingMinus7)
pred <- predict(model, newdata = results7, interval = "prediction", level = 0.95) %>% as.data.frame()
results7$pred <- pred$fit
results7$upperCI <- pred$upr
results7$lowerCI <- pred$lwr
results14 <- test14 %>% select(city, day031620, case.rate, casesTminus1.rate, casesTminus2.rate, weekend, walkingMinus7)
pred <- predict(model, newdata = results14, interval = "prediction", level = 0.95) %>% as.data.frame()
results14$pred <- pred$fit
results14$upperCI <- pred$upr
results14$lowerCI <- pred$lwr
metrics <- results7 %>%
group_by(city) %>%
summarize(MAE = round(mean(abs(case.rate - pred)) , 2)
, MAPE = round(mean(abs(case.rate - pred)/case.rate) , 2)
, CP = round(sum(case.rate >= lowerCI & case.rate <= upperCI ) / n() , 2)
) %>%
left_join( results14 %>%
group_by(city) %>%
summarize(MAE = round(mean(abs(case.rate - pred)) , 2)
, MAPE = round(mean(abs(case.rate - pred)/case.rate) , 2)
, CP = round(sum(case.rate >= lowerCI & case.rate <= upperCI ) / n() , 2)
)
, by = "city"
, suffix = c("_7d", "_14d")
)
#metrics %>% arrange(as.character(city)) %>% as.data.frame() %>% print()
allMetrics <- allMetrics %>% left_join(
metrics %>%
rename_at(vars(-city), function(x) {paste0(x, "_lmWalking7")})
, by = "city"
)pred <- predict(model, newdata = train, interval = "prediction", level = 0.95)
plotDF <- train %>%
select(city, day031620, case.rate) %>%
mutate(city = as.character(city)) %>%
cbind(pred) %>%
rename(fitted = fit
, lowerCI.fitted = lwr
, upperCI.fitted = upr
) %>%
reshape::melt(id = c('city', 'day031620')) %>%
# bring into forecasted case rates
rbind(results7 %>%
select(city, day031620, case.rate, pred, upperCI, lowerCI) %>%
rename(upperCI.pred = upperCI
, lowerCI.pred = lowerCI
) %>%
reshape2::melt(id = c('city', 'day031620'))
)
p <- ggplot(plotDF
, aes(day031620, value, group = variable, colour = variable)) +
geom_line(data = filter(plotDF, variable == 'case.rate'), linetype = "solid", color = 'black', alpha = 0.6) +
geom_line(data = filter(plotDF, variable == 'fitted'), linetype = "solid", color = 'red') +
geom_line(data = filter(plotDF, variable == 'pred'), linetype = "dashed", color = 'blue') +
# uncertainty band for fitted model
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.fitted')
, aes(ymin = filter(plotDF, variable == 'lowerCI.fitted')$value
, ymax = filter(plotDF, variable == 'upperCI.fitted')$value
)
, alpha = 0.3, color = NA
, fill = "red") +
# prediction band for forecast
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.pred')
, aes(ymin = filter(plotDF, variable == 'lowerCI.pred')$value
, ymax = filter(plotDF, variable == 'upperCI.pred')$value
)
, alpha = 0.3, color = NA
, fill = "blue") +
facet_wrap(. ~ city, ncol = 2) +
ggtitle('Forecast 7 Days') +
ylab('Case Rate per 100,000 People') +
xlab('Days since March 16, 2020') +
#ylim(-15,100) +
# add performance metrics
geom_label(data = metrics %>% mutate(MAPE_7d = paste0("MAPE = ", MAPE_7d))
, aes(label = MAPE_7d),
x = 0, y = 155, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = metrics %>% mutate(MAE_7d = paste0("MAE = ", MAE_7d))
, aes(label = MAE_7d),
x = 0, y = 125, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = metrics %>% mutate(CP_7d = paste0("CP = ", CP_7d))
, aes(label = CP_7d),
x = 0, y = 70, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
theme_classic() +
theme(legend.position = 'none')
p
plotDF <- train %>%
select(city, day031620, case.rate) %>%
mutate(city = as.character(city)) %>%
cbind(pred) %>%
rename(fitted = fit
, lowerCI.fitted = lwr
, upperCI.fitted = upr
) %>%
reshape::melt(id = c('city', 'day031620')) %>%
# bring into forecasted case rates
rbind(results14 %>%
select(city, day031620, case.rate, pred, upperCI, lowerCI) %>%
rename(upperCI.pred = upperCI
, lowerCI.pred = lowerCI
) %>%
reshape2::melt(id = c('city', 'day031620'))
)
p <- ggplot(plotDF
, aes(day031620, value, group = variable, colour = variable)) +
geom_line(data = filter(plotDF, variable == 'case.rate'), linetype = "solid", color = 'black', alpha = 0.6) +
geom_line(data = filter(plotDF, variable == 'fitted'), linetype = "solid", color = 'red') +
geom_line(data = filter(plotDF, variable == 'pred'), linetype = "dashed", color = 'blue') +
# uncertainty band for fitted model
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.fitted')
, aes(ymin = filter(plotDF, variable == 'lowerCI.fitted')$value
, ymax = filter(plotDF, variable == 'upperCI.fitted')$value
)
, alpha = 0.3, color = NA
, fill = "red") +
# prediction band for forecast
geom_ribbon(data = filter(plotDF, variable == 'lowerCI.pred')
, aes(ymin = filter(plotDF, variable == 'lowerCI.pred')$value
, ymax = filter(plotDF, variable == 'upperCI.pred')$value
)
, alpha = 0.3, color = NA
, fill = "blue") +
facet_wrap(. ~ city, ncol = 2) +
ggtitle('Forecast 14 Days') +
ylab('Case Rate per 100,000 People') +
xlab('Days since March 16, 2020') +
#ylim(-15,100) +
# add performance metrics
geom_label(data = metrics %>% mutate(MAPE_14d = paste0("MAPE = ", MAPE_14d))
, aes(label = MAPE_14d),
x = 0, y = 155, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = metrics %>% mutate(MAE_14d = paste0("MAE = ", MAE_14d))
, aes(label = MAE_14d),
x = 0, y = 125, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
geom_label(data = metrics %>% mutate(CP_14d = paste0("CP = ", CP_14d))
, aes(label = CP_14d),
x = 0, y = 70, hjust="inward", vjust="inward",
inherit.aes = FALSE) +
theme_classic() +
theme(legend.position = 'none')
p
allMetrics %>% select(city, starts_with("MAPE_7d")) %>%
arrange(as.character(city)) %>%
as.data.frame() %>%
print()## city MAPE_7d_lme MAPE_7d_lmeWeighted MAPE_7d_lmeWeightedWalking7
## 1 Atlanta 0.24 0.36 0.38
## 2 Baltimore 0.18 0.15 0.14
## 3 Boston 0.26 0.28 0.28
## 4 Chicago 0.33 0.33 0.33
## 5 Cleveland 0.28 0.21 0.21
## 6 Dallas 0.28 0.30 0.31
## 7 Denver 0.24 0.24 0.24
## 8 Houston 0.19 0.24 0.25
## 9 Indianapolis 0.21 0.18 0.18
## 10 London 0.15 0.19 0.19
## 11 Los Angeles 0.18 0.16 0.15
## 12 Memphis 0.51 0.53 0.54
## 13 Miami 0.25 0.26 0.25
## 14 Montreal 0.16 0.12 0.12
## 15 New York 0.15 0.15 0.15
## 16 Oklahoma 0.30 0.30 0.30
## 17 Phoenix 0.37 0.36 0.35
## 18 Pittsburgh 0.15 0.13 0.13
## 19 Portland 0.29 0.30 0.29
## 20 Sacramento 1.01 1.21 1.23
## 21 Seattle 0.42 0.48 0.48
## 22 Stockholm 0.17 0.10 0.10
## 23 Tampa 0.23 0.23 0.23
## 24 Toronto 0.12 0.10 0.11
## MAPE_7d_lm MAPE_7d_lmWalking7
## 1 0.34 0.34
## 2 0.17 0.17
## 3 0.28 0.28
## 4 0.33 0.33
## 5 0.25 0.24
## 6 0.28 0.28
## 7 0.24 0.23
## 8 0.20 0.22
## 9 0.21 0.20
## 10 0.16 0.17
## 11 0.18 0.17
## 12 0.51 0.51
## 13 0.23 0.23
## 14 0.16 0.15
## 15 0.16 0.16
## 16 0.28 0.28
## 17 0.37 0.37
## 18 0.13 0.13
## 19 0.28 0.28
## 20 1.12 1.15
## 21 0.45 0.45
## 22 0.15 0.16
## 23 0.22 0.23
## 24 0.12 0.12allMetrics %>% select(city, starts_with("MAE_7d")) %>%
arrange(as.character(city)) %>%
as.data.frame() %>%
print()## city MAE_7d_lme MAE_7d_lmeWeighted MAE_7d_lmeWeightedWalking7
## 1 Atlanta 6.17 6.88 7.18
## 2 Baltimore 4.02 3.25 3.18
## 3 Boston 5.35 5.25 5.34
## 4 Chicago 30.44 29.38 29.36
## 5 Cleveland 8.46 5.96 5.87
## 6 Dallas 7.87 7.95 7.99
## 7 Denver 13.37 13.12 13.13
## 8 Houston 2.30 2.48 2.58
## 9 Indianapolis 9.19 7.55 7.46
## 10 London 4.12 4.59 4.63
## 11 Los Angeles 2.74 2.41 2.36
## 12 Memphis 13.23 12.97 13.21
## 13 Miami 7.83 7.92 7.85
## 14 Montreal 0.92 0.73 0.75
## 15 New York 1.84 1.89 1.88
## 16 Oklahoma 21.09 20.37 19.94
## 17 Phoenix 6.64 6.27 6.22
## 18 Pittsburgh 3.19 2.65 2.58
## 19 Portland 5.12 4.72 4.70
## 20 Sacramento 6.21 6.79 6.76
## 21 Seattle 6.30 6.45 6.46
## 22 Stockholm 6.77 4.22 4.23
## 23 Tampa 4.74 4.71 4.76
## 24 Toronto 0.82 0.75 0.77
## MAE_7d_lm MAE_7d_lmWalking7
## 1 6.87 6.96
## 2 3.86 3.67
## 3 5.52 5.51
## 4 30.56 30.55
## 5 7.43 7.10
## 6 7.74 7.79
## 7 13.67 13.62
## 8 2.14 2.32
## 9 9.18 8.98
## 10 4.30 4.35
## 11 2.84 2.74
## 12 13.34 13.23
## 13 7.58 7.61
## 14 0.93 0.90
## 15 1.98 2.00
## 16 20.19 20.08
## 17 6.94 6.85
## 18 2.82 2.65
## 19 4.74 4.68
## 20 6.43 6.40
## 21 6.18 6.19
## 22 6.02 6.08
## 23 4.70 4.74
## 24 0.84 0.87allMetrics %>% select(city, starts_with("CP_7d")) %>%
arrange(as.character(city)) %>%
as.data.frame() %>%
print()## city CP_7d_lme CP_7d_lmeWeighted CP_7d_lmeWeightedWalking7 CP_7d_lm
## 1 Atlanta 0.71 0.14 0.14 0.86
## 2 Baltimore 1.00 0.43 0.43 1.00
## 3 Boston 1.00 0.29 0.29 1.00
## 4 Chicago 0.43 0.00 0.14 0.43
## 5 Cleveland 0.57 0.29 0.29 1.00
## 6 Dallas 0.71 0.43 0.43 0.71
## 7 Denver 0.57 0.00 0.00 0.57
## 8 Houston 1.00 0.57 0.57 1.00
## 9 Indianapolis 0.57 0.43 0.43 0.57
## 10 London 0.86 0.43 0.43 0.86
## 11 Los Angeles 1.00 0.57 0.57 1.00
## 12 Memphis 0.57 0.14 0.14 0.57
## 13 Miami 0.71 0.14 0.29 0.71
## 14 Montreal 1.00 1.00 1.00 1.00
## 15 New York 1.00 0.71 0.71 1.00
## 16 Oklahoma 0.57 0.00 0.00 0.57
## 17 Phoenix 1.00 0.14 0.14 1.00
## 18 Pittsburgh 1.00 0.57 0.57 1.00
## 19 Portland 0.86 0.29 0.29 1.00
## 20 Sacramento 0.86 0.29 0.29 0.86
## 21 Seattle 1.00 0.14 0.14 1.00
## 22 Stockholm 0.86 0.57 0.57 0.86
## 23 Tampa 1.00 0.29 0.29 1.00
## 24 Toronto 1.00 1.00 1.00 1.00
## CP_7d_lmWalking7
## 1 0.86
## 2 1.00
## 3 1.00
## 4 0.43
## 5 1.00
## 6 0.71
## 7 0.57
## 8 1.00
## 9 0.57
## 10 0.86
## 11 1.00
## 12 0.57
## 13 0.71
## 14 1.00
## 15 1.00
## 16 0.57
## 17 1.00
## 18 1.00
## 19 1.00
## 20 0.86
## 21 1.00
## 22 0.86
## 23 1.00
## 24 1.00allMetrics %>% select(city, starts_with("MAPE_14d")) %>%
arrange(as.character(city)) %>%
as.data.frame() %>%
print()## city MAPE_14d_lme MAPE_14d_lmeWeighted MAPE_14d_lmeWeightedWalking7
## 1 Atlanta 0.24 0.33 0.33
## 2 Baltimore 0.18 0.15 0.15
## 3 Boston 0.27 0.27 0.27
## 4 Chicago 0.25 0.25 0.25
## 5 Cleveland 0.24 0.17 0.17
## 6 Dallas 0.26 0.26 0.26
## 7 Denver 0.22 0.21 0.21
## 8 Houston 0.23 0.26 0.26
## 9 Indianapolis 0.21 0.20 0.20
## 10 London 0.16 0.18 0.18
## 11 Los Angeles 0.20 0.18 0.18
## 12 Memphis 0.48 0.48 0.49
## 13 Miami 0.39 0.40 0.39
## 14 Montreal 0.13 0.10 0.10
## 15 New York 0.15 0.16 0.16
## 16 Oklahoma Inf Inf Inf
## 17 Phoenix 0.37 0.37 0.37
## 18 Pittsburgh 0.16 0.13 0.13
## 19 Portland 0.23 0.26 0.26
## 20 Sacramento 0.95 1.14 1.16
## 21 Seattle 0.32 0.39 0.39
## 22 Stockholm 0.18 0.09 0.09
## 23 Tampa 0.27 0.28 0.28
## 24 Toronto 0.11 0.12 0.12
## MAPE_14d_lm MAPE_14d_lmWalking7
## 1 0.30 0.30
## 2 0.17 0.17
## 3 0.27 0.27
## 4 0.25 0.25
## 5 0.21 0.21
## 6 0.25 0.26
## 7 0.22 0.22
## 8 0.23 0.24
## 9 0.21 0.20
## 10 0.17 0.17
## 11 0.21 0.21
## 12 0.48 0.48
## 13 0.37 0.37
## 14 0.13 0.13
## 15 0.16 0.16
## 16 Inf Inf
## 17 0.36 0.35
## 18 0.13 0.13
## 19 0.24 0.24
## 20 1.05 1.08
## 21 0.35 0.35
## 22 0.16 0.16
## 23 0.26 0.26
## 24 0.13 0.13allMetrics %>% select(city, starts_with("MAE_14d")) %>%
arrange(as.character(city)) %>%
as.data.frame() %>%
print()## city MAE_14d_lme MAE_14d_lmeWeighted MAE_14d_lmeWeightedWalking7
## 1 Atlanta 6.86 7.50 7.60
## 2 Baltimore 4.76 3.68 3.61
## 3 Boston 6.22 5.68 5.74
## 4 Chicago 23.14 21.88 21.89
## 5 Cleveland 9.97 6.80 6.77
## 6 Dallas 8.72 8.21 8.21
## 7 Denver 15.86 15.08 15.10
## 8 Houston 4.09 4.05 4.07
## 9 Indianapolis 12.46 11.30 11.20
## 10 London 4.56 4.52 4.53
## 11 Los Angeles 3.82 3.34 3.30
## 12 Memphis 16.03 15.22 15.47
## 13 Miami 11.46 11.60 11.57
## 14 Montreal 0.85 0.66 0.68
## 15 New York 2.40 2.45 2.47
## 16 Oklahoma 21.90 19.66 18.95
## 17 Phoenix 8.96 8.97 8.92
## 18 Pittsburgh 4.43 3.46 3.41
## 19 Portland 5.20 5.43 5.40
## 20 Sacramento 7.28 7.74 7.74
## 21 Seattle 5.98 6.60 6.59
## 22 Stockholm 8.00 4.18 4.30
## 23 Tampa 5.08 5.16 5.19
## 24 Toronto 0.79 0.87 0.88
## MAE_14d_lm MAE_14d_lmWalking7
## 1 7.29 7.27
## 2 4.48 4.30
## 3 6.20 6.23
## 4 23.42 23.52
## 5 8.59 8.39
## 6 8.60 8.54
## 7 16.32 16.33
## 8 3.73 3.85
## 9 12.36 12.23
## 10 4.54 4.70
## 11 3.92 3.87
## 12 16.25 16.11
## 13 11.24 11.25
## 14 0.85 0.86
## 15 2.65 2.69
## 16 20.46 20.37
## 17 9.11 9.01
## 18 3.65 3.54
## 19 5.12 5.09
## 20 7.40 7.38
## 21 6.14 6.13
## 22 7.02 7.22
## 23 5.04 5.08
## 24 0.95 0.94allMetrics %>% select(city, starts_with("CP_14d")) %>%
arrange(as.character(city)) %>%
as.data.frame() %>%
print()## city CP_14d_lme CP_14d_lmeWeighted CP_14d_lmeWeightedWalking7
## 1 Atlanta 0.79 0.21 0.21
## 2 Baltimore 0.93 0.50 0.50
## 3 Boston 1.00 0.29 0.29
## 4 Chicago 0.36 0.07 0.14
## 5 Cleveland 0.57 0.29 0.29
## 6 Dallas 0.79 0.29 0.29
## 7 Denver 0.43 0.07 0.07
## 8 Houston 0.93 0.43 0.43
## 9 Indianapolis 0.50 0.21 0.21
## 10 London 0.86 0.50 0.50
## 11 Los Angeles 0.93 0.50 0.57
## 12 Memphis 0.50 0.14 0.14
## 13 Miami 0.50 0.07 0.14
## 14 Montreal 1.00 1.00 1.00
## 15 New York 1.00 0.64 0.64
## 16 Oklahoma 0.43 0.07 0.07
## 17 Phoenix 0.93 0.14 0.14
## 18 Pittsburgh 1.00 0.50 0.50
## 19 Portland 0.86 0.29 0.29
## 20 Sacramento 0.79 0.21 0.21
## 21 Seattle 0.93 0.07 0.07
## 22 Stockholm 0.93 0.43 0.43
## 23 Tampa 1.00 0.21 0.21
## 24 Toronto 1.00 1.00 1.00
## CP_14d_lm CP_14d_lmWalking7
## 1 0.86 0.86
## 2 0.93 1.00
## 3 1.00 1.00
## 4 0.43 0.43
## 5 0.86 0.86
## 6 0.79 0.79
## 7 0.43 0.43
## 8 1.00 1.00
## 9 0.50 0.50
## 10 0.86 0.86
## 11 0.93 0.93
## 12 0.50 0.50
## 13 0.50 0.50
## 14 1.00 1.00
## 15 1.00 1.00
## 16 0.50 0.50
## 17 0.93 0.93
## 18 1.00 1.00
## 19 0.93 0.93
## 20 0.79 0.79
## 21 1.00 0.93
## 22 0.93 0.93
## 23 1.00 1.00
## 24 1.00 1.00